PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
Student proficiency with transformational geometry after a college proof-based geometry class
Page: 655
This report explores pre-service teachers’ proficiency with concepts of transformational geometry at the end of a semester-long advanced geometry course. During the course, the instructor presented transformational geometry content, including congruence proofs, in an attempt to align with the Common Core State Standards for Mathematics. At the end of the course, the students, all pre-service teachers, appeared to mix ideas from the traditional approach involving triangle congruence criteria (SAS, ASA, SSS, AAS) and transformational approaches, and struggled with conceiving of transformation functions as objects. These difficulties appear to compound in their proof-writing attempts such that after citing appropriate transformational geometry ideas, such as the angle- or distance-preservation property, they would then supplement with congruence-based approaches in order to finish the proof. This has implications, especially for professional development, as this is the final mathematics class that these preservice teachers will take concerning transformational geometry prior to beginning their classroom instruction.